[Mithriil]

Asymptotics has been used to validate tons of statistical tools. This is just another tool being validated.

If you have a tool that you don't know works when data increases (n-> infinity), then you shouldn't use it.

So practicaly, I believe it has serious implications.

[jmalicki]

It's very much necessary but not sufficient. In real life the sample complexity matters a lot too, which is also asymptotics, but a more important one. E.g. how the central limit theorem is far more powerful than the law of large numbers.